Find `A and B` in the addition.
`A + A + A =BA`

Options

A. 1,5
B. 5,1
C. 1,2
D. 2,1

Explanation

To solve the equation \( A + A + A = BA \), we can break it down step by step.

### Step 1: Rewrite the equation
We can simplify the left side of the equation:
\[ 3A = BA \]
Here, \( BA \) represents a two-digit number where \( B \) is the tens digit and \( A \) is the ones digit.

### Step 2: Express \( BA \) in terms of \( A \) and \( B \)
The two-digit number \( BA \) can be expressed as:
\[ BA = 10B + A \]

### Step 3: Set up the equation
Now, we can set up the equation:
\[ 3A = 10B + A \]

### Step 4: Rearrange the equation
Subtract \( A \) from both sides:
\[ 3A - A = 10B \]
This simplifies to:
\[ 2A = 10B \]

### Step 5: Simplify the equation
Dividing both sides by 2 gives:
\[ A = 5B \]

### Step 6: Determine possible values for \( A \) and \( B \)
Since \( A \) and \( B \) are single-digit numbers (0 to 9), we can find suitable values for \( B \):
- If \( B = 1 \), then \( A = 5 \times 1 = 5 \)
- If \( B = 2 \), then \( A = 5 \times 2 = 10 \) (not a single-digit number)

Thus, the only valid solution is:
\[ B = 1 \quad \text{and} \quad A = 5 \]

### Step 7: Verify the solution
We can verify our solution:
\[ A + A + A = 5 + 5 + 5 = 15 \]
And \( BA = 10B + A = 10 \times 1 + 5 = 15 \) which is consistent.

### Final Answer
Thus, the values are:
\[ A = 5 \quad \text{and} \quad B = 1 \]

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